Methods and apparatus to obtain suspended particle information

ABSTRACT

Example methods and apparatus for obtaining suspended particle information are disclosed. A disclosed example method includes emitting light from a light source, dividing the light source into a first path and a second path, and directing the first path to a first container comprising a plurality of particles in a suspension material. The example method also includes directing the second path to a second container containing a suspension material devoid of particles, retrieving a first transmission value of the first path through the first container, and retrieving a second transmission value of the second path through the second container. The example method further includes directing the first and second paths to the second and first containers, respectively, retrieving a third transmission value of the first path through the second container, retrieving a fourth transmission value of the second path through the first container, and calculating a ratio of the first and second transmission values to the third and fourth transmission values to determine an indication of transmissivity for a given wavelength.

RELATED APPLICATION

This patent claims the benefit of U.S. Provisional Patent ApplicationNo. 61/197,192, entitled “Scanning Laser Assaying System,” filed on Oct.24, 2008, and U.S. Provisional Patent Application No. 61/211,141,entitled “Scanning Laser Assaying System,” filed on Mar. 26, 2009, whichare hereby incorporated by reference in their entireties.

TECHNICAL FIELD

The present disclosure relates to transmission based particlemeasurement, and in particular, to methods and apparatus to obtainsuspended particle information.

BACKGROUND

Identifying a number of objects suspended in a medium is typicallyaccomplished via particle counters employing a microscope to acquire animage of a section from the medium. Assuming that the particles remainin a homogeneous suspended state, a counted total of each of the objectswithin the section may be used to project a value representative of thedensity of objects in the medium. Automated particle sizing and countingon a microscopic scale began around 1954 with a Coulter Counter, whichemployed electrical sensing zone techniques. In particular, theparticles to be measured were dispersed in an electrolyte solution andpassed through a tube having a narrow aperture with electrodes on eitherside. The narrow aperture restricts the particles so that only a singleparticle passes through at one time through an electric field. As theparticles pass through the aperture, a resistance is measured, which isrelated to a corresponding particle size.

Techniques developed after the Coulter Counter evolved to reduce thetime required to measure particles and the efficiency at which particleswere measured via diffraction and/or scattering techniques using lightsources, such as single wavelength lasers. Generally speaking,diffraction techniques identify characteristic signatures of light aftera particle influences the incident light. Such characteristic signaturesmay be derived from ring-shaped intensity patterns indicative ofparticle size, in which closely situated rings identify correspondingparticles having a relatively larger size and widely situated ringsidentify corresponding particles having a relatively smaller size. Thediffraction techniques permitted an improved ability to measureparticles having smaller sizes than were capable via the CoulterCounter. Diffraction measurements allowed measurements down to particleshaving a 20 nano-meter (nm) diameter, but do not collect all of thescattered light, thereby limiting the resolution and sensitivity.Scattering techniques typically use a single detector, multipledetectors or an array of detectors, but only collect a fraction of thescattered light, which limit resulting resolution and/or sensitivity.

Scattering techniques to determine a size and/or distribution ofparticles include laser diffraction, dynamic light scattering, angledependent scattering, in which a fixed-wavelength laser is directed on asolution of particles and a single detector, multiple detectors or anarray of detectors is arranged to collect light scattered from thesolution. The techniques that analyze scattered light include dynamiclight scattering, angular dependent scattering, laser diffraction, andphoton cross correlation spectroscopy. Such techniques employ a singledetector, multiple detectors, or an array of detectors and may provideinformation indicative of the strength and distribution of the light toderive particle size and/or distribution information. Accordingly, thediffraction/light scattering techniques miss a substantial fraction ofthe total possible paths of light that are scattered by one or moreparticles in the sample.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A, 1B and 1C are example transmission-based particle measurementsystems to acquire suspended particle information.

FIG. 2 is a block diagram of an example transmission measurementcontroller that may be implemented by the example transmission-basedparticle measurement systems of FIGS. 1A, 1B and 1C.

FIG. 3 is an example plot of particle density versus bacteria particlesize for transmission-based measurement techniques.

FIGS. 4-6 and 8 are example processes that may be carried out usingtangible machine readable instructions to implement the exampletransmission-based particle measurement systems of FIGS. 1A, 1B and 1C.

FIG. 7A is a sensitivity comparison plot of particle density versusparticle size for scattering-based measurement techniques andtransmission-based measurement techniques.

FIG. 7B illustrate example resolution comparison plots of particledensity versus particle size between dynamic light scattering techniquesand transmission-based measurement techniques.

FIG. 9 is an example plot of particle density versus particle diameterfor manufacturer sourced polystyrene spheres using transmission-basedmeasurement techniques.

FIG. 10 is a schematic diagram of an example processor platform that mayexecute the example processes of FIGS. 4-6 and 8 and/or the exampletransmission measurement controller systems of FIGS. 1A, 1B, 1C and 2.

DETAILED DESCRIPTION

Identifying particle sizes of materials suspended in a solution (e.g.,in sprays, powders, suspensions, etc.) have several applications invarious industries. For example, some hydraulic equipment requires thatfluids and/or oils used under pressure conform to quality standardsrelated to foreign particle sizes and/or a density of foreign particles.In the event that such fluids and/or oils exceed a foreign particledensity threshold and/or a foreign particle size threshold, damage tothe hydraulic equipment may occur and/or result in potentially harmfulsafety concerns for equipment operators.

Additionally, industrial applications for determining particle sizesand/or particle densities in solution include de-ionized water and acidquality control for semiconductor manufacturing, and/or silt andsediment analysis. Further, industrial applications may include, withoutlimitation, biological particle studies, studies of oceanographic salinesamples, chemical abrasive quality control and specification, biologicalcellular analysis, virus analysis and/or virus identification.Suspension media may include liquid, gas or vacuum. Particle types mayinclude, but are not limited to atoms, molecules, metals, oxides,semiconductors and/or chemical compounds. Generally speaking, particlesizing and counting techniques are of particular interest in the fieldsof biology (e.g., biological weaponry identification), pharmaceuticalsand/or medicinal instrumentation. Particle size detection by one or morescattering-based techniques are typical methods employed by industryresearch personnel because of its robust implementation, ability to sizevarious types of particles, and availability of off-the-shelf hardware.However, scattering-based techniques exhibit one or more limitationsrelated to instrumentation sensitivity and particle size resolutionbased on, for example, the particle composition (e.g., metallicparticles, plastic particles, biological particles, etc.). Additionally,scattering-based techniques exhibit limitations related to measuringparticle sizes in circumstances where a solution may have a quantity ofdifferent sized particles.

The methods and apparatus described herein employ particle sizemeasurements, particle distribution measurements, absolute particlenumber measurements, and absolute particle density measurements vialight transmission rather than scattering-based techniques. As a result,particle sizes may be measured down to 10 nm or less, and up to 3000 nmor more, in which the range is a function of, in part, the lightsource(s), detector(s), and/or other components employed. Nonetheless,the ability to measure particle sizes as small as 10 nm facilitatespossibilities for the study of a wider variety of biological systems,such as viruses and proteins that scattering-based techniques fail toaccomplish. Additionally, while the scattering-based techniques identifyan estimated particle distribution based on a probability, the methodsand apparatus described herein identify absolute particle number (e.g.,total particle count) rather than the relative amount of each particletype. The methods and apparatus described herein also improve uponparticle identification by providing information related to a particlemajor axis and a minor axis. As a result, blood analysis using themethods and apparatus described herein provide biological particle size,shape and/or count information, including the ability to identify thepresence of bacteria, viruses, proteins and/or other particles andcells.

In the illustrated example of FIG. 1A, a transmission-based particlemeasurement system 100 includes a transmission measurement controller102, a variable wavelength laser 104 and a first mirror array 106 tobeam split and/or direct source laser light 108 from the examplevariable wavelength laser 104. The example first mirror array 106includes a linear slide 110, broadband mirrors 112, and opticallyidentical fused silica optical flats 114 a, 114 b to, in part,facilitate beam splitting. The example mirror array 106 also includesbeam dumps 116 and optically identical broadband mirrors 118. Inoperation, the source laser light 108 may be emitted from the variablewavelength laser 104 from any number of ports, such as a firstwavelength port 120, a second wavelength port 122 and a third wavelengthport 124. The example first wavelength port 120 emits source laser lighthaving a wavelength between 210 nm and 419 nm, the example secondwavelength port 122 emits source laser light 108 having a wavelengthbetween 420 nm and 709 nm, and the example third wavelength port 124emits source laser light 108 having a wavelength between 710 nm and 2300nm. Although the example variable wavelength laser source 104 includethree example ports 120, 122, 124, any other type of variable wavelengthlight source (e.g., laser source, broadband light source, etc.) may beemployed having greater or fewer output ports. For example, a lasersource may employ a single port capable of outputting a frequencybetween 210 nm and 2300 nm, and/or any other wavelength range. The lasersource may be the NT 342/UV by Ekspla Optics, which facilitates a laserpulse width of 4 ns and a repetition rate of 10 Hz. Additionally, the NT342/UV employs a pump beam to achieve wavelengths between 1064 nm and2300 nm.

The linear slide 110 is controlled by the example transmissionmeasurement controller 102 to select light from one or more ports 120,122, 124 and the broadband mirrors 112 on the slide 110 directs thelaser light 108 to the optically identical fused silica optical flats114 a, 114 b to create two optically identical laser beams 126 a (BeamA) and 126 b (Beam B). A collimator (not shown) may be used to fix thebeam radius at 1 millimeter (mm) prior to splitting the beam into twoidentical paths. The optically identical fused silica optical flats 114a, 114 b may operate as beamsplitters, in which the first flat 114 a maybe placed at a 45° angle of incidence and produce two 90° partialreflections, one at a front surface (F) and one at a back surface (B) ofthe first flat 114 a, and two 90° partial reflections, one at a backsurface (B) and one at the front surface (F) of the example second flat114 b. The two beams A 126 a and B 126 b are then directed, via theoptically identical broadband mirrors 118, toward a rotating sampleholder 128 affixed to motor-controlled rotating platform 130. Residuallight is absorbed in optical beam dumps 116. Beam A 126 a and Beam B 126b have substantially identical intensities, but are spatially separatedto reach corresponding spectrometer containers. Alternatively, Beam A126 a and Beam B 126 b may be generated by two separate light sources(e.g., two laser sources) and tuned to exhibit optical beamcharacteristics as similar as possible.

The example rotating sample holder 128 holds spectrometer containers(cuvettes) for sample A 132 and sample B 134, which may be implementedas quartz containers that hold de-ionized water or the material to beanalyzed. To eliminate errors and achieve improved performance resultsover scattering-based techniques (e.g., dynamic light scattering and/ordiffraction techniques), balance measuring techniques are applied to asample under test and a control sample. Errors may be introduced by, forexample, apparatus variation, differences in detector characteristics,amplifier characteristics, sample container properties, laser lightpower fluctuation (s), transient vibration(s) and/or atmosphericvariation(s). The balance measuring techniques include scanning thesample under test with a first laser beam and scanning the controlsample with a second laser beam derived from the same laser. While thefirst and second laser beams, discussed in further detail below, areconfigured by the example measurement system 100 to exhibit beams havingequal power, dimensions and/or polarization over all wavelengths, somevariation and/or uncertainty may arise in each laser beam, each detectorand/or any other environmental condition in which the examplemeasurement system 100 operates. The balance measuring techniquesinclude interchanging the sample under test and the control samplepositions so that the first laser beam strikes the control sample andthe second laser beam strikes the sample under test. As a result, thebalance measuring techniques eliminate potential uncertainty due tovariation of the example laser source 104, the mirror arrays 106, 138,Beam A 126 a, Beam B 126 b, containers for sample A 132 and sample B 134and/or one or more detectors, such as an example first photodetector 136a and an example second photodetector 136 b.

Balance measuring techniques may also include applying one or morefilters to the source laser light 108 before it is split by opticalflats 114 a, 114 b, thereby maintaining similar signal sizes of thelaser light 108 across all wavelengths of interest. The one or morefilters also minimize nonlinearities that may be associated with gainsand/or efficiency characteristics of the example first and secondphotodetectors 136 a, 136 b. Other detector characteristics addressed bybalance measurement techniques include matching the photodetectors sothat their gains, efficiencies and/or response times are similar and/orindependent of incident laser power from Beam A 126 a and/or Beam B 126b. Additionally, the balance measuring techniques may include selectingtwo containers for sample A 132 and sample B 134 to be as similar aspossible so that transmission difference between Beam A 126 a and Beam B126 b are minimized. Balance measuring techniques may also includeswapping the containers for sample A 132 and sample B 134 to account fordifferences in the transmission of the two containers.

Switching of the example spectrometer containers 132, 134 during thebalance measurement techniques may occur by rotating the example motorcontrolled rotating platform 130 by 180 degrees. Without limitation, oneor more broadband mirrors may be employed to switch Beam A 126 a andBeam B 126 b to strike either of the example sample A 132 or sample B134 to allow each sample to remain motionless. Measurements are made bythe first photodetector 136 a that corresponds to Beam A 126 a and thesecond photodetector 136 b that corresponds to Beam B 126 b. In theevent that one or more alternate photodetectors are employed toaccommodate one or more alternate ranges of laser wavelength (e.g., tobetter match ideal photodetector sensitivity operating range(s)), asecond mirror array 138 may be employed to direct laser light outputtoward a third detector 140 a and a fourth detector 140 b. For example,the first and second photodetectors 136 a, 136 b may be siliconphotodetectors that are ideally suited and/or responsive to laserwavelengths between 210 nm and 709 nm, but experience diminishedsensitivity for laser wavelengths at or above 710 nm. On the other hand,the third and fourth photodetectors 140 a, 140 b may be Germaniumphotodetectors that are ideally suited and/or responsive to laserwavelengths between 710 nm and 2300 nm, but experience diminishedsensitivity for laser wavelengths at or below 709 nm. For example,Germanium detectors are typically used for wavelengths between 710 nmand 2300 nm due to their superior efficiency as compared to Silicondetectors in such wavelength ranges.

While the illustrated example transmission-based particle measurementsystem 100 includes four example photodetectors 136 a, 136 b, 140 a, 140b, any number of photodetectors may be employed to accommodate one ormore specific laser light wavelength(s) of interest. Each photodetectoris communicatively connected to a first detector/amplifier 142 a and asecond detector/amplifier 142 b, which are further communicativelyconnected to the example transmission measurement controller 102. Unlikescattering-based measurement techniques, the example transmission-basedparticle measurement system 100 employs a single detector for eachincident laser light path to measure a resulting transmission power,thereby eliminating any need for an array of detectors in an effort tocapture light scattering for angles other than zero (θ≠0), as opposed toa zero angle of incidence (θ=0), which represents transmitted light.

For each selected wavelength (λ), the power for Beam A 126 a and Beam B126 b have similar power values P_(A) and P_(B), respectively, and alsohave similar polarization values. Initially, Beam A 126 a strikes theexample sample A 132 containing the particle sample under study and BeamB 126 b strikes the example sample B 134 containing a control suspensionfluid (e.g., de-ionized water). At least one benefit realized by thebalance measuring techniques when substantially simultaneously measuringtransmission through both containers 132, 134 is that any laser powerfluctuations from one laser pulse to the next laser pulse can bedivided-out during one or more ratio computations, as described infurther detail below. Corresponding photodetectors 142 a, 142 b receivetransmitted light after passing through each sample 132, 134 to producesignals D_(AP)(λ) and D_(BF)(λ), respectively. D_(AP)(λ) represents thesignal from the first detector 142 a from Beam A 126 a through theparticle sample with a suspension material (e.g., a suspension fluid, agas, etc.) at wavelength (λ), and D_(BF)(λ) represents the signal fromthe second detector 142 b from Beam B 126 b through the suspension fluidat wavelength (λ). The source wavelength (λ) is changed by a step value(e.g., 1 nm) and another measurement of the transmitted power throughthe particle sample and the suspension fluid is obtained as D_(AP)(λ+Δ)and D_(BF)(λ+Δ). The process of setting the laser wavelength, taking ameasurement in each path, and changing the laser wavelength by a stepvalue occurs for any number of iterations based on the startingwavelength (λ_(START)), the ending wavelength (λ_(FINISH)) and thewavelength step size.

As described above, to eliminate errors, the example transmission-basedmeasurement system 100 employs balance measuring techniques that switchthe location of example sample A 132 and sample B 134 via a 180 degreerotation after a first series of scanned laser wavelengths (a firstsweep). As a result, instead of Beam A 126 a striking example sample A132, Beam A 126 a now strikes example sample B 134 during a secondseries of scanned laser wavelengths (a second sweep). Similarly, insteadof Beam B 126 b striking example sample B 134, Beam B 126 b now strikesexample sample A 132 during the second sweep. Performing such balancingmeasuring techniques results in one or more benefits to the datacalculated by the example transmission measurement controller 102. Forexample, the balancing measurement techniques allow the exampletransmission measurement controller 102 to calculate an absolute numberof objects present in the sample under test rather than an estimate ofthe number and/or relative number of objects in the sample (which isindicative of results obtained when employing dynamic light scatteringtechniques). Additionally, the improved accuracy afforded by the balancemeasuring techniques allow the transmission measurement controller 102to calculate a major axis and a minor axis for non-spherical detectedparticles. In other words, by, in part, scanning each container during afirst sweep with Beam A 126 a and Beam B 126 b and then repeating thescan during a second sweep with each beam striking the oppositecontainer, a corresponding dynamic range and sensitivity of the exampletransmission measurement controller 102 is improved over that ofscattering-based techniques.

Balance measuring techniques may address one or more sources ofpotential error of the example transmission-based measurement system 100of FIG. 1A. For example, in the event of light source variation (e.g.,power fluctuation) from the example laser source 104 (or a broadbandlight source, as described below in connection with FIGS. 1B and 1C),the example balance measuring techniques can nullify and/or minimize theeffects of such variation on resulting particle measurement data.Further, because a single laser source is employed in the exampletransmission-based measurement system 100, any time-based powerfluctuation (s) (and/or other variation(s)) may be detectedsubstantially simultaneously at each detector to permit variationcancellation via the example balance measuring techniques (e.g., ratiocancellation). Other factors that may contribute to improved results inconnection with balance measuring techniques include, but are notlimited to, ensuring characteristic consistency between Beam A 126 a andBeam B 126 b. Characteristic consistency includes ensuring that Beam A126 a has a substantially identical path length as Beam B 126 b,ensuring that Beam A 126 a has a substantially identical attenuationcharacteristic(s) as Beam B 126 b, ensuring that Beam A 126 a has asubstantially identical power characteristic as Beam B 126 b and/orensuring that Beam A 126 a and Beam B 126 b have substantially identicalpolarization characteristics.

FIG. 1B illustrates another example transmission-based particlemeasurement system 150. In the illustrated example of FIG. 1B, abroadband light source 152 provides an incident light beam 154 a, 154 bdirected at a sample under test 156 and a control sample 158,respectively. Each incident light beam 154 a, 154 b may be implementedin any manner such as, but not limited to, an optical array(s) and/orfiber optic splitter(s). The example sample under test 156 may include acontainer, crucible and/or other optically transmissive container thatholds particles to be measured and/or that holds the control sample, asdescribed above. Similarly, the control sample 158 may hold thesuspension fluid, and both the sample under test 156 and control sample158 may be interchanged by, for example, rotating the sample holder 160by 180 degrees. Rotation of the example holder 160 may occur after anexample optical spectrometer (OS) and/or spectrum analyzer 162 a scans atransmitted beam 164 a for one or more wavelengths of interest (e.g., asweep of wavelengths of interest), and an example OS (and/or spectrumanalyzer) 162 b scans a transmitted beam 164 b substantiallysimultaneously at one or more wavelengths of interest. The exampletransmission-based particle measurement system 150 of FIG. 1B employsthe same measurement principles described herein, but uses the broadbandlight source for any number of desired wavelengths (e.g., infraredranges, ultraviolet ranges, etc.) rather than the tunable laser 104described in connection with FIG. 1A, and may allow particle measurementactivities to occur in a portable manner. Additionally, to discriminatefrom one wavelength to another wavelength, the exampletransmission-based particle measurement system 150 of FIG. 1B employsthe optical spectrometers (OSs) 162 a, 162 b, such as the Ocean OpticsHR4000 CG-UV-NIR. Although the methods and apparatus described hereinwill focus on the example of FIG. 1A, such descriptions are by way ofexample and not limitation.

FIG. 1C illustrates yet another example transmission-based particlemeasurement system 175. The illustrated example of FIG. 1C issubstantially similar to the system 150 shown in FIG. 1B and similarelements will maintain similar labels. In the illustrated example ofFIG. 1C, a broadband light source 152 provides an incident light beam154 directed at a sample under test 156. The example broadband lightsource 152 may include, but is not limited to a highly stable,stabilized solid-state light source and/or other broadband light source.The example sample under test 156 may include a container, crucibleand/or other optically transmissive container that holds particles to bemeasured and/or that holds the control sample, as described above. Thecontrol sample 158 may hold the suspension fluid, and both the sampleunder test 156 and control sample 158 may be interchanged by, forexample, rotating sample holder 160 by 180 degrees. Rotation of theexample holder 160 may occur after an example OS 162 scans a transmittedbeam 164 for one or more wavelengths of interest (e.g., a sweep ofwavelengths of interest). In operation, transmission versus wavelengthmeasurements are first performed for the particles in the test sample,then the samples are interchanged by moving or rotating the exampleholder 160 for the purpose of measuring transmission versus wavelengththrough the control sample.

FIG. 2 illustrates an example transmission measurement controller 102 infurther detail. In the illustrated example of FIG. 2, the transmissionmeasurement controller 102 includes a laser controller 202, a sampleplatform controller 204, a detector interface 206, calculation engines208, and a profile manager 210 communicatively connected to a profiledatabase 212. In example circumstances where the exampletransmission-based particle measurement system 150 of FIG. 1B isemployed, the light source controller may be, instead, an examplecontroller for the OS 162 and broadband light source 152. The examplecalculation engines 208 include an experimental extinction coefficientengine 214, a theoretical cross-section engine 216 and an inversionengine 218. In operation, the example light source controller 202 sets awavelength parameter for the example variable wavelength laser 104and/or other characteristics of the source laser light 108. For example,in addition to setting the output wavelength, the light sourcecontroller 202 may set an output power, a polarization and/or a pulseduration for the example variable wavelength laser 104.

The example platform controller 204 controls a rotation angle for theexample motor controlled rotating platform 130 shown in FIG. 1A. Asdescribed above, in the event that any given sample under test is to bemoved from Beam A 126 a to Beam B 126 b, or vice versa, the exampleplatform controller 204 engages one or more motors to interchange thetest sample with the control sample. The example detector interface 206provides signal conditioning for one or more detector amplifiers 142 a,142 b. Additionally, in the event that one or more detectors do notemploy a matched amplifier, the example detector interface 206 mayreceive detector input directly.

The example calculation engines 208 facilitate one or more calculationsusing the measured data collected after each sample of interest issubjected to one or more scans by the example variable wavelength laser104. As described above, the variable wavelength laser 104 is controlledby the laser controller 202 to emit a beam of laser energy at a startingwavelength (λ_(START)), dwell for a period of time to allow one or moredetectors 136 a, 136 b, 140 a, 140 b to obtain a transmissionmeasurement, and increment the laser wavelength (λ) by a step size foranother measurement. This process repeats until the finishing wavelength(λ_(FINISH)) is reached (a first sweep). After switching the examplecontainers 132, 134 or otherwise switching Beam A 126 a and Beam B 126 bto strike the opposite containers (thereby allowing the containers toremain motionless), a sweep from (λ_(START)) to (λ_(FINISH)) (a secondsweep) is repeated as part of the balancing measurement techniques. Thecollected data (i.e., the first and second sweep) is processed by theexample calculation engines 208 to determine one or more particle sizesin the sample under test, an absolute number (count) of particles ofeach size, one or more geometric indications of the detected particles(e.g., a major-axis, a minor-axis, etc.), a particle density value ofthe sample under test and/or a particle-size distribution of a sampleunder test.

To determine one or more particle sizes in the sample under test and/orto determine a particle density and/or particle count value of thesample under test, the example calculation engines 208 employ theexperimental extinction coefficient engine 214 to calculate anextinction coefficient as a function of wavelength. In particular, thetransmission through the sample is a function of particle size anddensity, which is further related to the total extinction cross sectionσ(λ). While the relationship between transmission and a correspondingwavelength provides information related to particle size, the exampletheoretical cross-section engine 216 is employed to obtain improvedsensitivity and resolution when combined and applied to a mathematicalinversion via the inversion engine 218. The example theoreticalcross-section engine 216 may employ Mie techniques to reveal the sizedependence of light transmission by particles, and includes a completeanalytical solution of Maxwell's equations for the transmission ofelectromagnetic radiation by spherical particles. Additionally oralternatively, the example theoretical cross-section engine 216 mayemploy other theoretical techniques including, but not limited to adiscrete dipole method(s) and finite element method(s). While an initialassumption that each particle is of spherical shape, the Mie theory maybe employed to account for geometries that have more than one dimension(e.g., a cylinder length and/or diameter, non-spherical particles,etc.). In circumstances where a particle under test has one or moredimensions, separate values for these dimensions will be detected,thereby indicating one or more signature geometric characteristics forthe sample under test. Generally speaking, the extinction coefficient(e.g., a first parameter) equals the product of the extinction crosssection (e.g., a second parameter) and the particle density (e.g., athird parameter). As such, knowledge, derivation and/or calculation oftwo parameters may yield the missing parameter.

Alternate modeling may be applied to the theoretical cross-sectionengine 216 and/or the inversion engine 218 to develop one or morelibraries of signature patterns, which may be stored and/or recalledfrom the example profile database 212. Generally speaking, while aspherical particle shape assumption may accurately identify particlesizes and/or particle distribution within a solution, one or moreprofiles may be used to identify the types of particles. For example,particle sizes of milk colloidals in skim and/or whole milk have beenverified with a resolution five times better than dynamic lightscattering techniques by using a spherical model. On the other hand, theE. Coli bacteria and bacteriophages are better modeled as cylindershaving a diameter and length. As the example transmission-based particlemeasurement systems 100, 150 and/or 175 are used, an increasing numberof signatures for biological systems, viruses and/or proteins may bestored as one or more profiles in the example profile database 212. Forinstance, the illustrated example plot 300 of FIG. 3 illustrates E. Colibacteria at an early stage and at a subsequent stage in which bacteriamultiplication has occurred.

Building further upon the relationship between the extinctioncoefficient, the extinction cross section and the particle density, oneor more alternate techniques may be applied to determine missing dataassociated with a sample under test. In another example, the extinctioncoefficients may be obtained via measurement and, instead of applyingMie theory to determine the corresponding extinction cross sections, theexample profile database 212 may be queried to obtain extinction crosssections for known viruses, bacteria, particles having a known index ofrefraction and/or particles having a known geometry. Based on themeasured extinction coefficients and the extinction cross sectionsobtained from the example profile database 212, an inversion may beapplied to obtain a corresponding particle density of the sample undertest.

In yet another example, in the event that a sample under test has aknown particle density, the corresponding extinction cross section maybe determined without applying Mie techniques by measuring the sampleunder test to obtain the extinction coefficients and then dividing themby the known particle density. Without limitation, this process may berepeated any number of times to build a more robust library (e.g.,stored in the example profile database 212) of extinction cross sectionvalues as a function of wavelength for each particle type. Furtherstill, for circumstances in which the sample under test has a knowngeometry and density, the corresponding index of refraction and/ordielectric constant of the sample under test may be determined (as afunction of wavelength) by measuring the sample for the extinctioncoefficients and then dividing them by the known geometry and density.

While the example transmission-based particle measurement system 100,150, 175 and transmission measurement controller 102 of FIGS. 1A, 1B, 1Cand 2 have been shown to identify particle sizes and densities ofmaterials suspended in a solution, one or more of the elements and/ordevices illustrated in FIGS. 1A, 1B, 1C and 2 may be combined, divided,re-arranged, omitted, eliminated and/or implemented in any other way.Further, the example transmission measurement controller 102, the firstmirror array 106, the variable wavelength laser 104, the linear slide110, the motor controlled rotating platform 130, the first photodetector136 a, the second photodetector 136 b, the second mirror array 138, thethird detector 140 a, the fourth detector 140 b, the firstdetector/amplifier 142 a, the second detector/amplifier 142 b, the lightsource 152, the rotating sample holder 160, the optical spectrometers162, 162 a, 162 b, the light source controller 202, the sample platformcontroller 204, the detector interface 206, the calculation engines 208,the profile manager 210, the profile database 212, the experimentalextinction coefficient engine 214, the theoretical cross section engine216 and/or the inversion engine 218 of FIGS. 1A, 1B, 1C and 2 may beimplemented by hardware, software and/or firmware. Thus, for example,any of the example transmission measurement controller 102, the firstmirror array 106, the variable wavelength laser 104, the linear slide110, the motor controlled rotating platform 130, the first photodetector136 a, the second photodetector 136 b, the second mirror array 138, thethird detector 140 a, the fourth detector 140 b, the firstdetector/amplifier 142 a, the second detector/amplifier 142 b, the lightsource 152, the rotating sample holder 160, the optical spectrometers162, 162 a, 162 b, the light source controller 202, the sample platformcontroller 204, the detector interface 206, the calculation engines 208,the profile manager 210, the profile database 212, the experimentalextinction coefficient engine 214, the theoretical cross section engine216 and/or the inversion engine 218 may be implemented by one or morecircuit(s), application specific integrated circuit(s) (ASIC(s)),programmable logic device(s) (PLD(s)), and/or field programmable logicdevice(s) (FPLD(s)), etc. When any of the appended apparatus claims areread to cover a purely software and/or firmware implementation, at leastone of the example transmission measurement controller 102, the firstmirror array 106, the variable wavelength laser 104, the linear slide110, the motor controlled rotating platform 130, the first photodetector136 a, the second photodetector 136 b, the second mirror array 138, thethird detector 140 a, the fourth detector 140 b, the firstdetector/amplifier 142 a, the second detector/amplifier 142 b, the lightsource 152, the rotating sample holder 160, the optical spectrometer 162a, 162 b, the light source controller 202, the sample platformcontroller 204, the detector interface 206, the calculation engines 208,the profile manager 210, the profile database 212, the experimentalextinction coefficient engine 214, the theoretical cross section engine216 and/or the inversion engine 218 are hereby expressly defined toinclude a tangible medium such as a memory, DVD, CD, etc. storing thesoftware and/or firmware. Further still, the example transmissionmeasurement controller 102, the first mirror array 106, the variablewavelength laser 104, the linear slide 110, the motor controlledrotating (or otherwise movable) platform 130, the first photodetector136 a, the second photodetector 136 b, the second mirror array 138, thethird detector 140 a, the fourth detector 140 b, the firstdetector/amplifier 142 a, the second detector/amplifier 142 b, the lightsource 152, the rotating (or otherwise movable) sample holder 160, theoptical spectrometer 162 a, 162 b, the light source (e.g., laser)controller 202, the sample platform controller 204, the detectorinterface 206, the calculation engines 208, the profile manager 210, theprofile database 212, the experimental extinction coefficient engine214, the theoretical cross section engine 216 and/or the inversionengine 218 of FIGS. 1A, 1B, 1C and 2 may include one or more elements,processes and/or devices in addition to, or instead of, thoseillustrated in FIGS. 1A, 1B, 1C and 2, and/or may include more than oneof any or all of the illustrated elements, processes and devices.

FIGS. 4 through 6 and 8 illustrate example processes that may beperformed to implement the example transmission-based particlemeasurement systems 100, 150, 175 and/or the example transmissionmeasurement controller 102 of FIGS. 1A, 1B, 1C and 2. The exampleprocesses of FIGS. 4 through 6 and 8 may be carried out by a processor,a controller and/or any other suitable processing device. For instance,the example processes of FIGS. 4-6 and 8 may be embodied in codedinstructions stored on any tangible computer-readable medium such as aflash memory, a CD, a DVD, a floppy disk, a read-only memory (ROM), arandom-access memory (RAM), a programmable ROM (PROM), anelectronically-programmable ROM (EPROM), and/or anelectronically-erasable PROM (EEPROM), an optical storage disk, anoptical storage device, magnetic storage disk, a magnetic storagedevice, and/or any other medium that can be used to carry or storeprogram code and/or instructions in the form of machine-readableinstructions or data structures, and that can be accessed by aprocessor, a general-purpose or special-purpose computer, or othermachine with a processor (e.g., the example processor platform P100discussed below in connection with FIG. 10). Combinations of the aboveare also included within the scope of computer-readable media.Machine-readable instructions comprise, for example, instructions and/ordata that cause a processor, a general-purpose computer, aspecial-purpose computer, or a special-purpose processing machine toimplement one or more particular processes. Alternatively, some or allof the example processes of FIGS. 4-6 and 8 may be implemented using anycombination(s) of ASIC(s), PLD(s), FPLD(s), discrete logic, hardware,firmware, etc. Also, one or more operations of the example processes ofFIGS. 4-6 and 8 may instead be implemented manually or as anycombination of any of the foregoing techniques, for example, anycombination of firmware, software, discrete logic, and/or hardware.Further, many other methods of implementing the example operations ofFIGS. 4-6 and 8 may be employed. For example, the order of execution ofthe blocks may be changed, and/or one or more of the blocks describedmay be changed, eliminated, sub-divided, or combined. Additionally, anyor all of the example processes of FIGS. 4-6 and 8 may be carried outsequentially and/or carried out in parallel by, for example, separateprocessing threads, processors, devices, discrete logic, circuits, etc.

The example process 400 of FIG. 4 begins with retrieving samplemeasurements from a particle sample under study and sample measurementsfrom a control sample (block 402). As described above, by comparing thetwo sets of data obtained via the balance measuring techniques (i.e.,one set for the particle sample and one set for the control sample andrepeating for alternate beams), any differences in detectorcharacteristics, amplifier characteristics and/or containercharacteristics may be eliminated, thereby improving a measure of theminimum signal that can be distinguished above noise levels(sensitivity), and improving a measure of observable detail(resolution). Additionally, by comparing the particle sample with thecontrol sample, any effect of the suspension fluid on the transmissioncharacteristics can be eliminated. To calculate a total extinctioncoefficient as a function of wavelength α(λ), the example experimentalextinction coefficient engine 214 calculates the ratios between theparticle sample and the control sample (block 404). The theoreticalcross-section engine 216 determines a scattering cross-section using,but not limited to Mie techniques, other theoretical techniques and/or adatabase of cross sections to reveal one or more size dependencies oflight transmission by the particles in the particle sample (block 406).Improved sensitivity and resolution is also realized by using theexperimentally determined extinction coefficient and the theoreticallydetermined scattering cross-section with a mathematical inversion (block408). The mathematical inversion may include, but is not limited to aFredholm Integral, as shown in Equation 1.

I(λ)=∫_(r) _(MIN) ^(r) ^(MAX) K(λ,r)ƒ(r)dr  Equation 1.

In the illustrated example Equation 1 when applied to the transmissiontechniques described herein, I(λ) represents the extinction coefficientα(λ) as a function of wavelength (λ) and ƒ(r) represents the particlesize distribution as a function of particle radius. The kernel, K(λ,r)is the theoretical extinction cross section as a function of wavelength(λ) and radius (r). The complex index of refraction as a function ofwavelength is an input to the calculation of the kernel K(λ,r). Each ofr_(MIN), r_(MAX) and dr are referred to herein as resolution parametersthat may affect a resolution of particle size distribution. Therepresentation K(λ,r) is sometimes referred to as an inversion kernelfunction because it contains all possible theoretical extinctioncross-sections for all wavelengths of scattering light and all particlesizes of interest. To obtain particle size and count information, aparticle size distribution (PSD) is determined from Equation 1, which isrepresented by ƒ(r). Generally speaking, the experimental extinctioncoefficient engine 214 facilitates calculation of I(λ), the theoreticalcross-section engine 216 facilitates calculation of K(λ,r), and the PSDcan be solved by way of a mathematical transformation, such as, but notlimited to Laplace transforms, Fourier transforms and/or matrixinversion techniques.

Inversion accuracy may be influenced by selected resolution parameters,such as r_(MIN), r_(MAX) and dr. In the event that a resolution isselected during the inversion that is too low, information from thesample measurements may be lost. For example, the extinction coefficientI(λ) would contain more information than what is extracted from theinversion. On the other hand, in the event that a resolution is selectedduring the inversion that is too high, numerical artifacts may result,such as multiple peaks where fewer actual peaks should exist. In thisexample circumstance, I(λ) would not contain the required informationneeded to achieve the resolution and a substantial error may result.While example Equation 1 may represent an integral form having a stepsize dr that can be infinitely small, numerically calculating Equation 1with real values reflects a resolution Δr equal to r_(MAX) minus r_(MIN)divided by a whole number of points. For example, for a range fromr_(MIN) of 1 nm to r_(MAX) of 1001 nm and 1000 points, the correspondingresolution Δr would be 1 nm.

Resolution parameter selection may be based on heuristics, input fromthe example profile manager 210 and/or based on the type of particle(s)believed to be in the sample under test. For example, if multiple-sizeparticles are present, the inversion resolution may need to be changed.For example, setting the inversion resolution, Δr, or particle diameterstep size, to a multiple of the resolution of the experimental data,(λ_(STEP)), or wavelength step size, may remove spurious inversionpeaks. This multiple may be a factor of two. Resetting the inversionresolution may also be indicated in other circumstances, including acase where particles homogeneous in size are present.

The example process 402 of FIG. 5 retrieves sample measurements from theparticle sample under study and sample measurements from the controlsample, such as pure and/or deionized water. In the illustrated exampleof FIG. 5, the transmission measurement controller 102 identifies astarting laser wavelength (λ_(START)), a final laser wavelength(λ_(FINISH)), a wavelength step size (λ_(STEP)) and a dwell time foreach step (block 502). Such settings may be stored in a profile, such asthe example profile manager 210 shown in FIG. 2 and/or one or more lasercontrol settings may be adjusted by a user. The identified lasersettings are provided to the example laser controller 202 to allow oneor more sequences of laser wavelengths to be emitted during the testingof the particle sample of interest (block 504) (e.g., during the firstsweep). To illustrate, the example laser controller 202 configures theexample variable wavelength laser 104 to emit laser radiation at astarting wavelength (λ_(START)) for the desired dwell period and, aftera measurement is acquired of laser radiation transmitted through eachcontainer (e.g., sample A 132 and sample B 134), the example lasercontroller 202 adjusts the laser wavelength based on the desired stepsize (λ_(STEP)). This sequence of laser emission, dwell time, andwavelength adjustment repeats from the starting wavelength to the finalwavelength.

The example sample platform controller 204 may control one or moredevices within the example first mirror array 106 and/or the examplesecond mirror array 138, such as a position of the example linear slide110, broadband mirrors 112, 118, 138, fused silica optical flats 114 a,114 b and/or the example beam dumps 116. The example sample platformcontroller 204 may also rotate a position of sample A 132 and sample B134 on the rotating sample holder 128 to allow the divided laser sourceenergy to strike each sample with Beam A 126 a and Beam B 126 b,respectively (block 506). However, rotation of the samples 132, 134 mayoccur after the first sweep is complete. Without limitation, the examplefirst mirror array 106 and second mirror array 138 may be adjusted todirect Beam A 126 a and Beam B 126 b toward the opposite containersafter the first sweep or in-between each wavelength scan, therebyallowing the containers 132, 134 to remain motionless. As describedabove, sample A 132 may hold the particle sample under test while sampleB 134 may hold the control sample (e.g., a suspension fluid without anyparticle matter therein).

Each of incident Beam A 126 a and Beam B 126 b strikes each sample A 132and B 134 to allow the laser energy to traverse through the containers.While some of the laser energy is absorbed, reflected and/or scatteredby each sample, a portion of the laser energy from each of Beam A 126 aand Beam B 126 b is transmitted through each container at the originalangle of incidence (i.e., zero degrees) and strikes each of the firstphotodetector 136 a (photodector A) and the second photodetector 136 b(photodetector B). Measurements from each photodetector are retrievedand saved as D_(AP) and D_(BF) (block 508), where D_(AP) represents theresulting signal detected by photodetector A after transmission throughthe particle sample (_(P)), and D_(BF) represents the resulting signaldetected by photodetector B after transmission through the control fluidsample (_(F)). If the finishing wavelength (λ_(FINISH)) has not beenreached (block 510), then the example laser controller 202 incrementsthe laser wavelength (λ) by the desired step size (block 512).

After a number of iterations of laser emission, dwell, measurement, andincrementing the laser wavelength from (λ_(START)) to (λ_(FINISH))(e.g., the first sweep), the example sample platform controller 204energizes the motor controlled sample holder to interchange the samplesso that Beam A 126 a strikes sample B 134 (i.e., the control sample) andBeam B 126 b strikes sample A 132 (i.e., the particle sample under test)(balance measurment) (block 514). The example laser controller 202 setsthe variable wavelength laser 104 to the starting wavelength (λ_(START))(block 516) and measurements are obtained from photodetector A 136 a andphotodetector B 136 b to obtain D_(AF) and D_(BP), respectively (block518). D_(AF) represents the resulting signal detected by photodetector Aafter transmission through the control fluid sample (_(F)) 134, andD_(BP) represents the resulting signal detected by photodetector B aftertransmission through the particle sample (_(P)) 132. If additionaladjustments to the example variable wavelength laser 104 are neededduring one or more steps from (λ_(START)) to (λ_(FINISH)) (block 520),then the example laser controller 202 makes the adjustment andincrements the wavelength of emitted laser light by the step size (block522).

In the example process 404 of FIG. 6, the experimental extinctioncoefficient engine 214 calculates a first ratio of particle signal tofluid signal for Beam A 126 a and Beam B 126 b. As described above, theexample variable wavelength laser 104 output 108 is split into two beamshaving similar powers P_(A) and P_(B) and similar polarization values.Prior to measuring the transmission of a test sample, the entiremeasurement process and ratio calculations described below are performedwith no samples and/or identical samples to ensure that the system 100,150, 175 is balanced. The fractions of input light power transmittedthrough each container are represented by Equations 2 and 3 shown below.

D _(AP)(λ)=∈_(A)(λ)T _(P)(λ)T _(F)(λ)P _(A)(λ)  Equation 2.

D _(BF)(λ)=∈_(B)(λ)T _(F)(λ)P _(B)(λ)  Equation 3.

In the illustrated example Equation 2 and Equation 3, D_(AP) representsthe resulting signal detected by photodetector A after transmissionthrough the particle sample (_(P)) (test sample), D_(BF) represents theresulting signal detected by photodetector B after transmission throughthe suspension fluid (_(F)) (control sample), ∈_(A) represents theefficiency of photodetector A 136 a, ∈ _(B) represents the efficiency ofphotodetector B 136 b, T_(P)(λ) represents the fraction of input lightpower transmitted by the particles at a given wavelength, and T_(F)(λ)represents the fraction of input light power transmitted through thesuspension fluid at the given wavelength. As described above, theparticle sample (_(P)) and the suspension fluid (_(F)) containers areinterchanged (balance measuring) so that another set of measurementstherethrough can be made. Similar to Equations 2 and 3, the fractions ofinput light power transmitted through the particle sample (_(P)) andsuspension fluid (_(F)) are represented by Equations 4 and 5 shownbelow.

D _(AF)(λ)=∈_(A)(λ)T _(F)(λ)P _(A)(λ)  Equation 4.

D _(BP)(λ)=∈_(B)(λ)T _(P)(λ)T _(F)(λ)P _(B)(λ)  Equation 5.

In the illustrated example Equation 4 and Equation 5, D_(AF) representsthe resulting signal detected by photodetector A after transmissionthrough the suspension fluid (_(F)) (control sample) and D_(BP)represents the resulting signal detected by photodetector B aftertransmission through the particle sample (_(P)). The exampleexperimental extinction coefficient engine 214 calculates a first ratioof the particle signals to the suspension fluid signals for Beam A andBeam B, respectively (block 602). Similarly, after the full range ofwavelengths are scanned from (λ_(START)) to (λ_(FINISH)), the exampleexperimental extinction coefficient engine 214 calculates a second ratioof the suspension fluid signals to the particle signals for Beam A andBeam B, respectively (block 604). The four signals from Equations 2, 3,4 and 5 as a result of the first sweep of wavelengths and the secondsweep of wavelengths from the balance measuring are used to calculate aratio of ratios R(λ) as shown in Equation 6.

$\begin{matrix}{{R(\lambda)} = {\frac{\frac{D_{AP}(\lambda)}{D_{BF}(\lambda)}}{\frac{D_{AF}(\lambda)}{D_{BP}(\lambda)}} = {\left( {T_{P}(\lambda)} \right)^{2}.}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

The transmissivity versus wavelength T_(P)(λ) due to the particles inthe particle sample 132 may be computed as shown in Equation 7 (block606).

$\begin{matrix}{{T_{P}(\lambda)} = {\sqrt{R(\lambda)} = {\sqrt{\frac{\frac{D_{AP}}{D_{BF}}}{\frac{D_{AF}}{D_{BP}}}} = {^{{- {\alpha {(\lambda)}}}t}.}}}} & {{Equation}\mspace{14mu} 7} \\{{{\alpha (\lambda)}l} = {{- {\ln \left( \frac{\frac{D_{AP}}{D_{BF}}}{\frac{D_{AF}}{D_{BP}}} \right)}} = {{- \frac{1}{2}}{{\ln \left( \frac{\frac{D_{AP}}{D_{BF}}}{\frac{D_{AF}}{D_{BP}}} \right)}.}}}} & {{Equation}\mspace{14mu} 8}\end{matrix}$

In the illustrated example of Equation 8, α(λ) represents the extinctioncoefficient and l represents the path length through the sample (i.e.,the length of the light passing through the particle liquid (material),but not the container widths). Example Equation 8 is used to calculatethe experimental value of the extinction coefficient at each wavelength.In theory, the extinction coefficient versus wavelength α(λ) due to theparticles is related to the total theoretical scattering cross-sectionσ_(i)(λ) of particle type i by Equation 9.

α(λ)=Σ_(j)σ_(j)(λ)n _(j)  Equation 9.

In the illustrated example Equation 9, n_(j) is the number of particlesper unit volume of type j, and the summation Σ_(j) is over all particletypes. Equation 8 illustrates calculating the extinction coefficientfrom the data for each wavelength (block 608). Equation 9 is inverted toobtain the number of particles per unit volume n_(j) of each type j. Ifthere is a continuum of particle sizes, then the extinction coefficientis represented as shown below in example Equation 9b, where n(r) is theparticle size distribution.

α(λ)=∫σ(λ,r)n(r)dr  Equation 9b.

Briefly returning to FIG. 4, the example theoretical cross-sectionengine 216 employs one or more theoretical techniques such as, but notlimited to Mie theory and/or a database to model the total cross sectionof the particle sample under test (block 406). Generally speaking, Mietheory is a complete analytical solution of Maxwell's equations for thescattering of electromagnetic radiation by spherical particles. WhileMie theory techniques typically perform with optimum results when theratio of the particle diameter to the incident laser wavelength are onthe order of unity, the methods and apparatus described herein may beemployed to determine a major and minor axis of the particles understudy by, in part, employing a range of wavelengths. Unlike particlesizing techniques that utilize scattering, in which the laser wavelength(λ) is fixed and the scattering angle (θ) is varied or scattered lightis measured at one or more fixed angle other than zero, the methods andapparatus described herein utilize transmission behavior of the laserenergy, in which the laser wavelength (λ) is varied and transmittedlight is measured at an angle (θ) fixed at zero with respect to theincident light detection. As described above, monitoring thetransmission of the laser energy improves size, density, count and/orgeometry determinations by utilizing a single photodiode for eachincident (i.e., zero angle with respect to the incident light direction)laser beam, rather than an array of photodiodes that are typicallyrequired when employing scattering techniques. Generally speaking,scattering techniques can never capture all of the scattered light,whereas the transmitted light signal is always sensitive to all of thescattered light. The transmitted light signal is ultimately a functionof light scattered at all directions, but scattering techniques,including dynamic light scattering and diffraction, detect only afraction of the scattered light. Generally speaking, as a number ofadditional photodiodes are added to a measurement system in an attemptto capture more of the scattered light, a corresponding uncertainty inthe measured data accumulates, which may lower any resulting sensitivityand/or resolution. By applying Mie theory techniques to lighttransmission detection at multiple wavelengths and at a zero degreescattering angle, a theoretical extinction cross-section versuswavelength σ(λ,r) may be obtained for each particle radius by firstcalculating Mie coefficients, as shown in Equation 10.

$\begin{matrix}{{\sigma \left( {\lambda,r} \right)} = {\frac{2\pi}{k^{2}}{\sum\limits_{n = 1}^{\infty}{\left( {{2n} + 1} \right){\left( {{a_{n}\left( {\lambda,r} \right)} + {b_{n}\left( {\lambda,r} \right)}} \right).}}}}} & {{Equation}\mspace{14mu} 10}\end{matrix}$

In the illustrated example of Equation 10, a_(n) and b_(n) are the Miecoefficients, and the extinction cross-section σ(λ,r) may be defined asshown in Equation 10. In Equation 10, k=2π/λ.

In some examples the Mie calculations may be performed by thetheoretical cross-section engine 216 by way of one or more applications,such as MIEV0 by Warren J. Wiscombe and one or more graphical outputs ofthe Mie calculations may be performed by the theoretical cross-sectionengine 216 to illustrate general particle size trends and/or occasionswhere the incident laser light wavelength is at or near the size of thecorresponding particle diameters. Generally speaking, plotted Miecalculations illustrate major and minor oscillatory behavior, peaksand/or valleys depending on the particle size, the index of refractionof the particle and/or the index of refraction of the surrounding medium(e.g., fluid, gas, spray, etc.). Additionally, relatively smalloscillatory ripples may occur when transmitted laser light pathsinterfere with each other. Ripples can occur because some light energyis transmitted through each particle (e.g., sphere) with no internalreflections therein along path P₀, and some light is transmitted througheach particle after internal reflections within the particle that exitin the same direction as P₀, but have a different phase and path length,P_(n). Accordingly, more than one P_(n) can exist, which may result inobserved interference between P₀ and any number of P_(n) paths, therebyshowing up as ripples in the extinction cross section σ(λ,r) whenplotted.

Using the Mie calculations to infer a particle density as a function ofsize using data obtained without the balancing techniques describedabove may provide one or more indications of general particle size,however such results alone may not reveal a range of particle sizesand/or densities of each particle size within the sample under test witha suitable resolution, sensitivity and/or absolute density information.In other words, results from only the Mie calculations using dataobtained without proper balancing techniques may be limited in theirability to provide results that enable the accurate identification ofparticle sizes, geometries and/or an ability to identify a particle type(e.g., viruses, bacteria, proteins, cells, etc.). The methods andapparatus described herein utilize the balance measuring techniques, theMie calculation results, and the experimental results with a tailoredmathematical inversion to enable calculation of any number particlesizes that may be present in the sample under test, in which theresulting sizes have a resolution that is significantly better thanscattering-based particle sizing techniques. Additionally, due to, inpart, the balance measuring techniques, the methods and apparatusdescribed herein reveal an absolute number of objects in the sampleunder test rather than a relative number of objects, as provided byscattering-based methods (e.g., dynamic light scattering). Further, thebalance measuring techniques facilitate the ability to identify a majorand minor axis of non-spherical particles and the ability to distinguishmultiple sizes in the sample under test. The balance measurementsfurther improve a dynamic range and yield a sensitivity that isapproximately one million times more sensitive than dynamic lightscattering-based methods, as shown in FIG. 7A, and a resolution that isapproximately five times better than results achieved with dynamic lightscattering-based methods, as shown in FIG. 7B.

In the illustrated example of FIG. 7A, a technique comparison plot 700is shown to illustrate capabilities of dynamic light scatteringtechniques (dashed line 702) and the transmission-based methods andapparatus described herein (see circles in FIG. 7A). The example plot700 of FIG. 7A includes a y-axis 704 of particle density (concentration)per mL, and an x-axis 706 of particle size in nm. While the results fromdynamic light scattering illustrate an ability to distinguish particleconcentrations at a lower threshold of approximately 10⁹ particles permL, the transmission-based methods and apparatus described hereinillustrate sensitivities as low as approximately 10³ particles per mL.Additionally, the plot 700 illustrates successful application of thetransmission-based methods and apparatus described herein to detect goldparticles 708, E. Coli particles 710, and relatively low concentrationsof virus particles 712 and polystyrene particles 714. The methods andapparatus described herein analyze the particle sample under test at arange of wavelengths to expose the sizes, densities, counts and/orgeometries of particles that may be present therein.

In the illustrated example of FIG. 7B, another technique comparison plot750 is shown to illustrate capabilities regarding resolution for dynamiclight scattering techniques (upper plot 752) and the transmission-basedmethods (lower plot 754) and apparatus described herein. The exampledynamic light scattering techniques 752 and transmission-based methods754 share a similar x-axis 756 to further illustrate improvements toresolution capabilities of the transmission-based methods 754. Forexample, single spherical casein micelles of milk protein are shown as apeak 758 using dynamic light scattering techniques 752 that areapproximately five times wider than a peak 760 derived after employingtransmission-based methods 754. As a result, the methods and apparatusdescribed herein related to transmission-based techniques for obtainingsuspended particle information allow a finer degree of detail that maynot be revealed when employing dynamic light scattering techniques. Theexample plots 752, 754 of FIG. 7B also illustrate a relative sensitivityimprovement of transmission-based techniques over dynamic lightscattering. In particular, the peak 760 of spherical casein miscelles ofmilk protein having a density of 2.5×10⁻¹⁶ nm⁻³ (762) roughlycorresponds to 1.3×10⁻⁸ volume percent (764), thereby indicating asensitivity factor improvement of approximately one billion.

The example process 408 of FIG. 8 begins with selecting a spatialparticle size model (block 802) from any number of spatial models thatmay be available in the example profile manager 210. In somecircumstances, a general type of particle present in the particle sampleunder test may be known, but the specific sizes and/or densities presenttherein may not be known. For example, if the particle sample under testis known to contain polystyrene spheres from a manufacturing supplier ofsuch spheres, then a spherical spatial model may be selected (block804). On the other hand, if the general type of particle present in theparticle sample under test is not known, the spherical spatial model maybe a suitable starting point because it can provide results indicativeof a major and minor axis of the particles present. As the exampletransmission-based particle measurement system 100, 150, 175 is usedwith different types of particles, the example profile manager 210 maystore characteristic spatial signature patterns of the differentparticle types. Each virus, bacteria and/or manufacturing particle(e.g., abrasive particles) may exhibit unique spatial signaturecharacteristics that can later be identified with the aid of a selectedspatial model (e.g., a rod-shaped model, etc.) and/or stored databasemodel. For circumstances where the particle type is known to besomething other than a sphere (block 802), an alternate spatial modelmay be selected (block 806).

Particles also include a characteristic complex dielectric constantproperty and/or complex index of refraction. If the particle sampleunder test is known to contain dielectric properties similar topolystyrene and/or the dielectric constant is generally undetermined(block 808), then a dielectric model associated with polystyrene may beselected to establish a baseline measurement of the particles (block810). However, if the particles in the sample under test are generallyknown to have an alternate dielectric value, then an alternatedielectric model may be selected that is more similar to the particlesunder test (block 812). Major categories of particle types includebiological particles, metals and/or oxides.

The example inversion engine 218 assigns, based on the index ofrefraction and/or dielectric constant of the particles under test, thetheoretical results generated by the example theoretical cross-sectionengine 216 to the inversion kernel function K(λ,r) (block 814), and theexperimental results generated by the example experimental extinctioncoefficient engine 214 are assigned to the Fredholm Integral functionI(λ) at each scanned wavelength (λ) (block 816). The particle sizedistribution, n(r), as a function of radius, r, is represented by ƒ(r).The inversion is solved (e.g., example Equation 1) for ƒ(r), whichcontains sizing and density information (block 818). In discrete form,n(r) is represented by a column vector with elements (j), where eachelement of the column vector is a particle density. The index j for thiscolumn vector is the radius and/or type of the particle. Additionally,the inversion kernel function K(λ,r) is represented by an i×j matrixwhere the i index is the scattering wavelength and the j index is theparticle size and/or type. As such, an (i, j) matrix element refers tothe extinction cross section (ECSC) of a particle size and/or type j atlight wavelength i.

The inversion kernel function K(λ,r) is calculated (e.g., MIEV0.f code,etc.) with an assumed radius of the spherical particle having index ofrefraction (m) at wavelength (λ) to yield an ECSC. Valid ECSC resultsare retained as any number of assumed radii are used when solving theFredholm integral equation (e.g., Equation 1) (e.g., solving for a rangeof particle sizes that can be expected in a sample particle under test).Additionally, ƒ(r) contains the particle size and count information, andcan be visualized as a column matrix with j elements, where the range ofj is determined by the limits of integration shown in Equation 1. If oneof the elements exists in the example matrix, then a particle existshaving the corresponding particle size of the represented matrixposition.

To illustrate further, example Equation 1 is the integral of theinversion kernel function K(λ,r)*ƒ(r) across a limited range of expectedparticle sizes r_(min) to r_(max) (with step size dr) that could existin the particle sample. During the integration, ECSC values are pickedout for particle size(s) that are contained in the particle sizedistribution ƒ(r) from the kernel K(λ,r). The result is an extinctioncoefficient for a particle sample having size distribution ƒ(r), whichis represented as I(λ).

Having calculations for K(λ,r) and data for I(λ) results in an inversionhaving a number of possible solutions, some of which are not relevantbecause the inversion is an ill-pose problem. Mathematically, themathematical inversion may be represented by the matrix of exampleEquation 13.

$\begin{matrix}{\begin{bmatrix}I_{1} \\\ldots \\I_{t} \\\ldots\end{bmatrix} = \left. {\begin{bmatrix}k_{11} & \ldots & k_{1j} & \ldots \\\ldots & \ldots & \ldots & \ldots \\k_{i\; 1} & \ldots & k_{ij} & \ldots \\\ldots & \ldots & \ldots & \ldots\end{bmatrix}\begin{bmatrix}f_{1} \\\ldots \\f_{j} \\\;\end{bmatrix}}\Rightarrow{{{Inversion}\begin{bmatrix}f_{1} \\\ldots \\f_{j} \\\ldots\end{bmatrix}}.} \right.} & {{Equation}\mspace{14mu} 13}\end{matrix}$

In the form of example Equation 13, if given ƒ_(j), the matrixmultiplication of K_(ij)*ƒ_(j) picks out resultant ECSC values that giveI=ΣK_(ij)ƒ_(j) represented in matrix form as I=Kƒ. However, when I isgiven by the data and f represents the unknown densities of eachparticle size the matrix equation of I=Kƒ is an overdetermined system ofequations, which may be solved for ƒ via a least squares minimizationmethod designed to minimize the sum of squares of the residuals as shownin example Equation 14.

∥Kƒ−I∥²  Equation 14.

In the illustrated example Equation 14, K may be ill-posed or singular,which may further result in multiple solutions for ƒ. In the event thatone or more solutions of ƒ are oscillatory, no physical meaning isassociated with it. To filter out one or more nonphysical solutions, theexample inversion engine 218 applies a regularization matrix (block820). Example Equation 15 illustrates an example regularization matrixaΓ applied to Equation 14 as shown in Equation 15.

∥Kf−I∥²+∥aΓƒ∥²  Equation 15.

The example regularization matrix aΓ where a is a regularizationparameter may be applied via any method including, but not limited tothe Tikhonov Regularization method. Including the regularization factorallows the physical solutions to be revealed while discarding one ormore non-meaningful solutions. A Tikhonov matrix Γ may include anidentity matrix I and regularization parameter a having a value of 1.

Example output 900 from an inversion and regulization process is shownin FIG. 9. In the illustrated example of FIG. 9, a y-axis 902 representsa density of particles present per cubic nanometer, and an x-axis 904represents a particle diameter (two times the radius). Manufacturersourced particles were confirmed to be 771 nm diameter spheres with a 5%deviation. The example transmission-based particle measurement system100 identified a particle distribution 906 having a first peak of 771 nm(908) and a second peak of 807 nm (910), each of which fall within thestated manufacturer tolerance of 5%. The particle size distribution 906provides particle count information because the y-axis 902 reveals howmany particles are present per unit volume at each diameter and all thevalues in the particle size distribution 906 may be summed. Multiplyingthe summed density distribution by the volume of the sample reveals atotal number of particles in the sample.

FIG. 10 is a schematic diagram of an example processor platform P100that may be used and/or programmed to implement any or all of theexample transmission measurement controller 102, the first mirror array106, the variable wavelength laser 104, the linear slide 110, the motorcontrolled rotating platform 130, the first photodetector 136 a, thesecond photodetector 136 b, the second mirror array 138, the thirddetector 140 a, the fourth detector 140 b, the first detector/amplifier142 a, the second detector/amplifier 142 b, the light source 152, therotating sample holder 160, the optical spectrum analyzer 162, the lasercontroller 202, the sample platform controller 204, the detectorinterface 206, the calculation engines 208, the profile manager 210, theprofile database 212, the experimental extinction coefficient engine214, the theoretical cross section engine 216 and/or the inversionengine 218 of FIGS. 1A, 1B, 1C and 2. For example, the processorplatform P100 can be implemented by one or more general-purposeprocessors, processor cores, microcontrollers, etc.

The processor platform P100 of the example of FIG. 10 includes at leastone general-purpose programmable processor P105. The processor P105executes coded instructions P110 and/or P112 present in main memory ofthe processor P105 (e.g., within a RAM P115 and/or a ROM P120). Theprocessor P105 may be any type of processing unit, such as a processorcore, a processor and/or a microcontroller. The processor P105 mayexecute, among other things, the example processes of FIGS. 4-6 and 8 toimplement the example methods and apparatus described herein.

The processor P105 is in communication with the main memory (including aROM P120 and/or the RAM P115) via a bus P125. The RAM P115 may beimplemented by dynamic random access memory (DRAM), synchronous dynamicrandom access memory (SDRAM), and/or any other type of RAM device, andROM may be implemented by flash memory and/or any other desired type ofmemory device. Access to the memory P115 and the memory P120 may becontrolled by a memory controller (not shown). The example memory P115may be used to implement the example profile database 212 of FIG. 2.

The processor platform P100 also includes an interface circuit P130. Theinterface circuit P130 may be implemented by any type of interfacestandard, such as an external memory interface, serial port,general-purpose input/output, etc. One or more input devices P135 andone or more output devices P140 are connected to the interface circuitP130.

Although certain example methods, apparatus and articles of manufacturehave been described herein, the scope of coverage of this patent is notlimited thereto. On the contrary, this patent covers all methods,apparatus and articles of manufacture fairly falling within the scope ofthe appended claims either literally or under the doctrine ofequivalents.

1. A method to identify particle information, comprising: emitting lightfrom a light source; dividing the light source into a first path and asecond path; directing the first path to a first container containing aplurality of particles in a suspension material; directing the secondpath to a second container containing a suspension material devoid ofparticles; retrieving a first transmission value of the first paththrough the first container; retrieving a second transmission value ofthe second path through the second container; directing the first andsecond paths to the second and first containers, respectively;retrieving a third transmission value of the first path through thesecond container; retrieving a fourth transmission value of the secondpath through the first container; and calculating a ratio of the firstand second transmission values to the third and fourth transmissionvalues to determine an indication of transmissivity for a givenwavelength.
 2. A method as defined in claim 1, wherein the transmissionvalues are retrieved at about a zero degree angle of exit with respectto the angle of incidence between each of the first and second paths andthe first and second containers.
 3. A method as defined in claim 1,wherein directing the first and second paths to the second and firstcontainers, respectively, further comprises interchanging a position ofthe first and second containers.
 4. A method as defined in claim 1,wherein directing the first and second paths to the second and firstcontainers, respectively, further comprises adjusting a mirror arraythat receives the emitted light source.
 5. A method as defined in claim1, wherein determining the transmissivity further comprises retrievingthe first, second, third and fourth transmission values for a pluralityof wavelengths to yield a transmissivity as a function of wavelength. 6.A method as defined in claim 5, further comprising applying Mie theoryto calculate an extinction cross section as a function of wavelengthindicative of particle size and shape.
 7. A method as defined in claim6, further comprising employing an inversion function to determineparticle size and particle number.
 8. A method as defined in claim 6,further comprising employing an inversion function to determine particledensity.
 9. A method as defined in claim 7, wherein the inversionfunction comprises an inversion with values across a range ofwavelengths and across a range of particle sizes.
 10. A method asdefined in claim 9, further comprising applying a regularization factorto identify a physical solution of the inversion function.
 11. A methodas defined in claim 5, further comprising calculating an extinctioncoefficient as a function of wavelength from the transmissivity.
 12. Amethod as defined in claim 1, wherein the given wavelength comprises aplurality of wavelengths from an ultra-violet range to an infraredrange.
 13. A method as defined in claim 1, wherein calculating the ratioof the first and second transmission values to the third and fourthtransmission values further comprises determining an extinctioncoefficient for the given wavelength.
 14. A method as defined in claim13, further comprising using the extinction coefficient at eachwavelength with a known particle density of the first container todetermine an extinction cross section as a function of wavelength.
 15. Amethod as defined in claim 1, further comprising using data indicativeof an extinction cross section as a function of wavelength from adatabase and applying an inversion to the extinction coefficient todetermine a particle density of the first container.
 16. A method asdefined in claim 1, wherein a particle density of the first container isknown, further comprising using the extinction coefficient and theparticle density to determine the dielectric constant or an index ofrefraction for the particle in the first container.
 17. A method asdefined in claim 1, wherein a particle density of the first container isknown, further comprising dividing the extinction coefficient by theparticle density to derive an extinction cross section.
 18. An apparatusto identify particle information, comprising: a light source capable ofemitting light comprising a plurality of wavelengths; an optical arrayto divide emitted light from the light source to a first path and asecond path; a platform to orient a first container and a secondcontainer with either the first path or the second path; a first andsecond photodetector to receive a first and second transmitted path atabout a zero angle of exit with respect to the angle of incidence to thefirst and second container; a detector interface to receive transmissionsignals from the first and second photodetectors at a first time and asecond time, each associated with a first wavelength; and a calculationengine to compute the particle information based on the receivedtransmission signals.
 19. An apparatus as defined in claim 18, whereinthe calculation engine further comprises an experimental extinctioncoefficient engine to balance out errors associated with the receivedtransmission signals.
 20. An apparatus as defined in claim 19, whereinthe experimental extinction coefficient engine calculates ratios of thereceived transmission signals to determine a transmissivity as afunction of wavelength.
 21. An apparatus as defined in claim 19, whereinthe experimental extinction coefficient engine calculates ratios of thereceived transmission signals to determine an extinction coefficient asa function of wavelength.
 22. An apparatus as defined in claim 18,further comprising a light source controller to sweep the light sourcethrough the plurality of wavelengths and invoke the experimentalextinction coefficient engine at each of the plurality of wavelengths tocalculate an extinction coefficient based on a ratio of the transmissionsignals to minimize particle information error.
 23. An apparatus asdefined in claim 22, further comprising a theoretical cross sectionengine based on Maxwell equations and applied to the ratio oftransmission signals for each wavelength in the sweep to extractparticle information.
 24. An apparatus as defined in claim 23, furthercomprising an inversion engine to extract a physical solution from anoutput of the applied Maxwell equations and to discard nonphysicalsolutions.
 25. An apparatus as defined in claim 18, wherein the firstand the second photodetectors are wavelength dependent.
 26. An apparatusas defined in claim 18, wherein the first and second photodetectorscomprise at least one of a spectrum analyzer or a spectrum analyzer. 27.An apparatus as defined in claim 18, wherein the detector interfacemeasures the first and second transmitted paths as a light power as afunction of wavelength.
 28. A method to identify particle size, countand density information, comprising: receiving a first light beamattenuated by a first container having particles, and receiving a secondlight beam attenuated by a second container having a control medium;measuring a first and a second signal at a first and second detector,the first and second detectors receiving the first and second lightbeams, respectively, at a first wavelength; directing the first andsecond light beams to the second and first containers, respectively;measuring a third and a fourth signal at the first and second detector;and calculating an extinction coefficient based on the first, second,third and fourth signals, the total extinction cross section indicativeof particle size, count and density.
 29. A method as defined in claim28, further comprising minimizing an error component of the extinctioncoefficient to improve a sensitivity of the first and second detector bycalculating a ratio of the first and second signals to the third andfourth signals.
 30. A method as defined in claim 28, wherein the firstand second detectors are silicon photodetectors for a first range ofwavelengths, and germanium photodetectors for a second range ofwavelengths.
 31. A method as defined in claim 28, further comprisingapplying Mie theory to calculate the total extinction cross section fora plurality of wavelengths to determine a size dependency of theplurality of particles as a function of wavelength.
 32. A method asdefined in claim 31, further comprising applying an inversion using theMie calculations to determine particle diameter, count and concentrationinformation associated with the particles in the first container.
 33. Amethod as defined in claim 28, further comprising using the extinctioncoefficient at each wavelength with a known particle density of thefirst container to determine an extinction cross section as a functionat each wavelength.
 34. A method as defined in claim 28, furthercomprising using data indicative of an extinction cross section as afunction of wavelength from a database and applying an inversion to theextinction coefficient to determine a particle density of the firstcontainer.
 35. A method as defined in claim 28, wherein a particledensity of the first container is known, further comprising using theextinction coefficient and the particle density to determine thedielectric constant.
 36. A method as defined in claim 28, wherein aparticle density of the first container is known, further comprisingdividing the extinction coefficient by the particle density to derive anextinction cross section.
 37. A method to measure particles in asuspension material, comprising: directing a light source to a firstcontainer having particles in a suspension material; measuring anattenuated portion of the light source at a first time, the attenuatedportion at the first time transmitted from the light source through thefirst container; directing the light source to a second container havinga control material; measuring an attenuated portion of the light sourceat a second time, the attenuated portion at the second time transmittedfrom the light source through the second container; and calculating aratio of the measurement from the first time and the second time toidentify an extinction coefficient.
 38. A method as defined in claim 37,further comprising measuring the attenuated portion at the first timeand the second time for a plurality of wavelengths.
 39. A method asdefined in claim 38, wherein an optical signal analyzer measures theattenuated portion of the light source at the first time and the secondtime for each of the plurality of wavelengths.
 40. A method as definedin claim 38, further comprising calculating the extinction coefficientas a function of wavelength.
 41. A method as defined in claim 37,wherein the light source comprises a broadband light source having aplurality of wavelengths.
 42. A method as defined in claim 37, furthercomprising using the extinction coefficient at each wavelength with aknown particle density of the first container to determine an extinctioncross section as a function of wavelength.
 43. A method as defined inclaim 37, further comprising applying Mie theory to obtain theextinction cross section as a function of wavelength and applying aninversion to the extinction coefficient as a function of wavelength todetermine a particle density of the first container.
 44. A method asdefined in claim 42, further comprising saving the extinction crosssection as a function of wavelength to a database, the saved extinctioncross section information associated with the particle density of thefirst container.
 45. A method as defined in claim 44, further comprisingassociating the saved extinction cross section information with aparticle dielectric constant indicative of the particles in the firstcontainer.
 46. A method as defined in claim 44, further comprisingassociating the saved extinction cross section information with aparticle refractive index indicative of the particles in the firstcontainer.
 47. A method as defined in claim 37, further comprising usingdata indicative of an extinction cross section as a function ofwavelength from a database and applying an inversion to the extinctioncoefficient to determine a particle density of the first container. 48.A method as defined in claim 37, wherein a particle density of the firstcontainer is known, further comprising using the extinction coefficientand the particle density to determine at least one of a dielectricconstant or an index of refraction for the particles in the firstcontainer.
 49. A method as defined in claim 37, wherein a particledensity of the first container is known, further comprising dividing theextinction coefficient by the particle density to derive an extinctioncross section.
 50. A method as defined in claim 49, further comprisingderiving the extinction cross section as a function of wavelength for aknown type of particle in the first container.